Abstract
Let $Y$ be a real algebraic variety. We are interested in determining the supremum, $\beta(Y)$, of all nonnegative integers $n$ with the following property: For every $n$-dimensional compact connected nonsingular real algebraic variety $X$, every continuous map from $X$ into $Y$ is homotopic to a regular map. We give an upper bound for $\beta(Y)$, based on a construction involving complexification of real algebraic varieties. In some cases, we obtain the exact value of $\beta(Y)$.
Citation
Wojciech Kucharz. Łukasz Maciejewski. "Complexification and homotopy." Homology Homotopy Appl. 16 (1) 159 - 165, 2014.
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